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operators with positive kernels

Proceedings of the Edinburgh Mathematical Society (1)

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CRITERIA FOR THE BOUNDEDNESS AND COMPACTNESS OF INTEGRAL TRANSFORMS WITH POSITIVE KERNELS
A. Meskhi
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 2 / June 2001

Published online by Cambridge University Press:

20 January 2009, pp. 267-284
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The necessary and sufficient conditions that guarantee the boundedness and compactness of integral operators with positive kernels from $L^p(a,b)$ to $L^q_{\nu}(a,b)$, where $p,q\in(1,\infty)$ or $0lt q\leq1lt plt\infty$, for a non-negative Borel measure $\nu$ on $(a,b)$ are found.
AMS 2000 Mathematics subject classification: Primary 46B50; 47B34; 47B38